In each of 3-6, the relation R is an equivalence relation on A. As in Example 8.3.5, first find the specified equaivalence classes. Then state the number of distinct equivalenvce classes for R and list them.
R is defined on A as follows:
Equivalence classes:, , , 
To find the distinct equivalence classes of R.
The relation R is an equivalence relation on the set A.
Let us first group the ordered pairs in R that have at least one common element (with at least one of the other elements in the group).
is true if and only if is a multiple of 3 if and only if x and y differ by 0,3,6 or 9 (as the elements are between -4 and 5, including).
Thus when x and y differ by 0, 3, 6 or 9.
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